Question : Three pipes, A, B, and C can fill an empty cistern in 2, 3, and 6 hours respectively. They are opened together. After what time should B be closed, so that the cistern gets filled in exactly 1 hr 15 min?
Option 1: 20 min
Option 2: 45 min
Option 3: 30 min
Option 4: 15 min
Correct Answer: 30 min
Solution :
Given:
Pipes A, B, and C can fill empty cisterns in 2, 3, and 6 hours respectively.
Now,
Total time taken 1 hr 15 min = $\frac{5}{4}$hrs = 1.25 hrs
Let total work = LCM (2, 3, 6) = 6
Work done by A in 1 hr = $\frac{6}{2} = 3$ units
Work done by B in 1 hr = $\frac{6}{2} = 2$ units
Work done by C in 1 hr = $\frac{6}{6} = 1$ unit
Work done by A, B, and C in 1 hr = 3 + 2 + 1 = 6 units
A, B, and C are opened together but after $x$ hours pipe B is closed.
So, according to the question
$x$ × work done by A, B, and C in 1 hour + $(1.25-x)$ × work done by A and C in 1 hour = 6
$⇒ 6x + (1.25-x) × 4 = 6$
$⇒ 2x + 5 = 6$
$⇒ x = 0.5$ hours $= 30$ min
Hence, the correct answer is 30 min.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates BrochureYour Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.